Singly heavy tetraquark resonant states with multiple strange quarks

We systematically investigate the S-wave singly heavy tetraquark systems containing two or three strange quarks, Qss̄s̄, Qns̄s̄ and Qss̄n̄( Q=c,b,n=u,d ), within the constituent quark potential model. We solve the four-body Schrödinger equation using the Gaussian expansion method (GEM) and identify resonances via the complex scaling method (CSM). There are no bound states below the lowest two-meson thresholds. We obtain several compact resonances with JP=0⁺,2⁺ in Qss̄s̄, and JP=2⁺ in Qns̄s̄ and Qss̄n̄. The pole positions are mainly distributed around $7.0-7.2$ GeV (bottom) and $3.7-3.9$ GeV (charm), with widths from a few to several tens of MeV. These resonances decay into Dₛη^ ,D₍ₛ₎^*ϕ,Dₛ^*K^* and Dₛ^*K̄^* (and their bottom counterparts), providing targets for future experimental searches.